Good questions as it might be overcharging. This needs to be rule out before replacing the battery but the battery does need to be replaced because of the leakage.
Also using a voltmeter put one lead on either the positive or negative and take the other lead touch the battery case in various places if you get a voltage reading you have an electrically leaky battery case. I have personally seen this multiple times over the years. What it is, is that the plastic case become conductive.